Question Number 65788 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $${Explicit}\:\:\:{f}\left({a}.{b}.{c}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{sec}\left({x}−{a}\right)}{{b}.{cosx}\:+\:{c}.{sinx}}\:{dx} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 65786 by ~ À ® @ 237 ~ last updated on 04/Aug/19 $$\:{Shows}\:{that}\:\:\mid\Gamma\left(\mathrm{1}+{ix}\right)\mid^{\mathrm{2}} =\frac{\pi}{{xsinh}\left(\pi{x}\right)}\:\:\:\:\:\:{with}\:\Gamma\left({z}\right)=\int_{\mathrm{0}_{} } ^{\infty} \:{t}^{{z}−\mathrm{1}} {e}^{−{t}} {dt} \\ $$$${Then}\:{Prove}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:\mid\Gamma\left(\mathrm{1}+{ix}\right)\mid^{\mathrm{2}}…
Question Number 131320 by mohammad17 last updated on 03/Feb/21 Answered by mr W last updated on 04/Feb/21 $$\mathrm{2}:\:\mathrm{1}+\mathrm{1}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{36}} \\ $$$$\mathrm{3}:\:\mathrm{1}+\mathrm{2},\:\mathrm{2}+\mathrm{1}\:\Rightarrow\frac{\mathrm{2}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{18}} \\ $$$$\mathrm{4}:\:\mathrm{2}+\mathrm{2},\:\mathrm{3}+\mathrm{1},\:\mathrm{1}+\mathrm{3}\:\Rightarrow\frac{\mathrm{3}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\mathrm{5}:\:\mathrm{2}+\mathrm{3},\:\mathrm{3}+\mathrm{2},\:\mathrm{1}+\mathrm{4},\:\mathrm{4}+\mathrm{1}\:\Rightarrow\frac{\mathrm{4}}{\mathrm{36}}=\frac{\mathrm{1}}{\mathrm{9}} \\…
Question Number 250 by 123456 last updated on 25/Jan/15 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{2}{x}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} =\mathrm{0} \\ $$ Answered by prakash jain last updated on 17/Dec/14 $$\frac{{dy}}{{dx}}={u} \\…
Question Number 248 by sushmitak last updated on 25/Jan/15 $$\mathrm{If}\:{f}\left({x}\right)=\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{2}} \left({x}+\pi/\mathrm{3}\right)+\mathrm{cos}\:{x}\:\mathrm{cos}\:\left({x}+\pi/\mathrm{3}\right) \\ $$$$\mathrm{and}\:\:{g}\left(\mathrm{5}/\mathrm{4}\right)=\mathrm{1}\:\mathrm{then}\:\:{gof}\left({x}\right)=? \\ $$ Answered by 123456 last updated on 17/Dec/14 $${f}\left({x}\right)=\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{2}}…
Question Number 65782 by Rio Michael last updated on 03/Aug/19 $$\:{Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{2}} \left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}{x}\:+\:\mathrm{4}\right)^{\mathrm{7}} {dx} \\ $$$${hence}\:{show}\:{that}\:\:\frac{{d}}{{dx}}\left({coshx}\right)\:=\:{sinh}\:{x} \\ $$ Commented by mathmax by abdo last…
Question Number 247 by 123456 last updated on 25/Jan/15 $$\mathrm{A}:\mathrm{C}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{B}:\mathrm{C}\vee\mathrm{A}\:\mathrm{is}\:\mathrm{false} \\ $$$$\mathrm{C}:\mathrm{B}\:\mathrm{is}\:\mathrm{truth} \\ $$$$\mathrm{then}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{F}\:\mathrm{is}\:\mathrm{truth}\:\mathrm{or}\:\mathrm{false}? \\ $$$$\mathrm{F}:\left(\mathrm{A}\wedge\mathrm{B}\right)\vee\left(\mathrm{A}\wedge\mathrm{C}\right)\vee\left(\mathrm{B}\wedge\mathrm{C}\right)\: \\ $$ Answered by prakash jain last…
Question Number 245 by 123456 last updated on 25/Jan/15 $$\mathrm{A}=\left\{\mathrm{0},\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mathrm{B}=\left\{\mathrm{0},\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{9}\right\} \\ $$$$\mathrm{C}=\left\{\mathrm{1},\mathrm{2},\mathrm{4},\mathrm{5},\mathrm{7},\mathrm{8},\mathrm{10}\right\} \\ $$$$\mid\left(\mathrm{A}\cup\mathrm{B}\right)\cap\left(\mathrm{B}\cup\mathrm{C}\right)\mid \\ $$ Answered by mreddy last updated on 17/Dec/14…
Question Number 65781 by gunawan last updated on 03/Aug/19 $$\mathrm{If}\:{xyz}\:\neq\:\mathrm{0}\:\mathrm{and}\:{x}+{y}+{z}=\mathrm{0} \\ $$$${a}=\mathrm{10}^{{z}} \\ $$$${b}=\mathrm{10}^{{y}} \\ $$$${c}=\mathrm{10}^{{x}} \\ $$$$\mathrm{then} \\ $$$${a}^{\left(\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}\right)} .\:{b}^{\left(\frac{\mathrm{1}}{{z}}+\frac{\mathrm{1}}{{x}}\right)} .{c}^{\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}\right)} =… \\ $$$${a}.\:\mathrm{0}.\mathrm{001}…
Question Number 65778 by mathmax by abdo last updated on 03/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:{e}^{−{n}^{\mathrm{2}} } \left({n}+\mathrm{1}\right)^{{n}!} \\ $$ Commented by mathmax by abdo last updated on…